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An example of using $\Delta_1$ terms in Boolean valued analysis
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 1, pp. 47-63 Cet article a éte moissonné depuis la source Math-Net.Ru

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Syntactic tools related to $\Delta_1$ terms are demonstrated by application to Boolean valued analysis. As an example, the question is considered of what approaches to defining the field $\mathbb R$ of reals and what complete Boolean algebras $B$ provide the explicit inclusion $\mathbb R^\land\subset\mathbb R$ inside the Boolean valued universe $\mathbb V^{(B)}$. 
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A. E. Gutman. An example of using $\Delta_1$ terms in Boolean valued analysis. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 1, pp. 47-63. http://geodesic.mathdoc.fr/item/VMJ_2012_14_1_a4/

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